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Metamath Proof Explorer

Theorem neeqtrrd

Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012)

Ref Expression
Hypotheses neeqtrrd.1 
|- ( ph -> A =/= B )
neeqtrrd.2 
|- ( ph -> C = B )
Assertion neeqtrrd 
|- ( ph -> A =/= C )

Proof

Step Hyp Ref Expression
1 neeqtrrd.1 
 |-  ( ph -> A =/= B )
2 neeqtrrd.2 
 |-  ( ph -> C = B )
3 2 eqcomd 
 |-  ( ph -> B = C )
4 1 3 neeqtrd 
 |-  ( ph -> A =/= C )